Some New Families of Fourth Order Methods

Nazir Ahmad Mir, Hassan Jawaid, Saarang Soomro


In this article, we derive four new familes of fourth order iterative methods using the binomial approximation in certain existing three families of methods. The convergence analysis of the methods is discussed. Per iteration, the new families of methods require two evaluations of the given function and one of its derivative. Thus each of the four families has computational efficiency 1.587 which is better than many of the existing iterative methods. Some numerical examples are tested to check the efficiency and performance of the new families of methods.


Iterative methods; Computational Efficiency; Predictor-corrector methods; Convergence Order; Nonlinear equations

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